Mechanical Properties of Solids

Mechanical Properties Of Solids Elasticity: It is the property property of a body by virtue vi rtue of which it tends to regain its i ts original size and shape after the applied force is removed. Plasticity: It is the the inability inabi lity of a body in regaining regai ning its i ts original status on the removal removal of the deforming forces.

Elastic deformation:  After withdrawal of force, the material regains its original shape and an d size. si ze.

Plastic deformation:  After withdrawal of force, the material does not regain its original size and shape.

Stress: Restoring force per unit area Types of Stress Normal Stress: When the elastic restoring restoring force or deforming force acts perpendicular perpendicul ar to the area, the the stress is called call ed normal stress. Normal Normal stress can be sub-divided sub-divi ded into the following categories: Tensile Stress: When there is an increase i ncrease in the length le ngth or the extension of the body in the direction di rection of the force force applied, appli ed, the stress stress set up is called cal led tensile tensil e stress. Compressive Stress: When there is a decrease in i n the length or the compression of the body due to the force applied, applie d, the stress stress set up is called cal led compressive stress. Tangential or Shearing Stress: When the elastic el astic restoring force or deforming force acts parallel to the surface surface area, the stress stress is called cal led tangential stress.

Strain : Deformation amount/original dimension

Shear strain =

Within elastic elastic limits, li mits, θ is small. Therefore, Shear strain = tan θ θ

Hooke’s law:  Stress is proportional to Strain Stress = k  ×  × Strain [Where, k  =   = Modulus of elasticity]

Stress-strain graph For a wire

When the material does not regain its original dimension, it is said to have a permanent set, and the deformation is said to be plastic deformation. Stress-strain curve c urve for elastomers: elastomers:

They do not obey Hooke’s law, and always return to their original shape.

Young’s modulus of elasticity ( Y )

The Young's modulus of an experimental wire is given by .

Bulk modulus modulus of elasticity elasticit y ( B )

Compressibility: It is the reciprocal of bulk modulus.

Modu Modulus lus of rigid rigidity ity ( )

Δ

Poisson's ratio(σ ) = lateral strain/longi strain/longitudinal tudinal strain Poisson's ratio(σ ) is a unitless and dimensionless dimensionl ess quantity. A metallic rod expands on heating and the thermal strain strain developed devel oped in the rod is given gi ven by Δ . When a rod, fixed at both the ends by supports, supp orts, is heated, it exerts a force on both the supports. The force exerted exerted on the supports is given gi ven by F = YαΔt A. Application of Elasticity Elasticity The metallic parts in machinery are never subjected to stress beyond their elastic limits; l imits; else, they may get permanently deformed. The thickness of the metalli metallic c rope used in cranes depends on the elastic el astic limit of the material of the rope and the factor of safety. Bridges are designed design ed in such a way w ay that they they do not bend much or break under the load of heavy traffic, traffic, force of strong strong wind wi nd or their own ow n weights. wei ghts.

Poisson’s Poisson’s ratio rati o

 = Elastic energy is given by: Elastic energy stored in the wire on elongating it by a length l =